Electric power transmission and distribution systems or networks comprise high-voltage tie lines for connecting geographically separated regions, medium-voltage lines, and substations for transforming voltages and for switching connections between lines. Power generation and load flow in a network with several substations is controlled by an energy management system. For managing the network, it is desirable to determine a state of the network, in particular load flows and stability margins. Measurements of average RMS (root mean square) values of voltages, currents, active power and reactive power flowing in the network and/or measurements of voltage and current phasors are made at various places in the network and collected by substation automation (SA) systems and by a supervisory control and data acquisition (SCADA) system. In recent times, devices and systems for measuring voltage and current phasors at different locations of a network at exactly the same time and for collecting them at a central data processor have become available. Phasors collected from throughout the network in combination provide a snapshot of the electrical state of the network.
In order to maximally utilise a line, it is desirable to maximise the amount of transmitted power. This amount is limited by several factors, in particular a thermal limit and an electrical limit. Currently, these limits are taken into account by making assumptions about the electrical parameters of the line and by calculating a maximum power flow. A temperature of the line, which depends on weather conditions, may be measured by temperature sensors distributed along the line. Such measurements are however not representative for the entire line. Due to the shortcomings of existing systems, power lines are operated with overly conservative limits on transmitted power.